make sure the option “Background App Refresh” is on for the app. Go to Settings > General > Background App Refresh, make sure it is on at the top, then scroll down and find the Home Assistant app and make sure the toggle is on. Other than that, no there’s no way to autostart an app on booting the device. Welcome to the Apple ecosystem. Also, it’s Home Assistant (more specifically Home Assistant Companion App for Apple), NOT Hassio iOS App. The name Hassio is dead.